Images of function and distribution spaces under the Bargmann transform
Abstract
We consider a broad family of test function spaces and their dual (distribution) space. The family includes Gelfand-Shilov spaces, a family of test function spaces introduced by S. Pilipovic. We deduce different characterizations of such spaces, especially under the Bargmann transform and the Short-time Fourier transform. The family also include a test function space, whose dual space is mapped by the Bargmann transform bijectively to the set of entire functions.
Cite
@article{arxiv.1409.5238,
title = {Images of function and distribution spaces under the Bargmann transform},
author = {Joachim Toft},
journal= {arXiv preprint arXiv:1409.5238},
year = {2016}
}
Comments
53 pages. This version dates from June 2016. The main different between this version with the previous January 2016 version is that Proposition 1.2 for classifications of Gelfand-Shilov distributions with STFT is extended in full range. This leads to that Section 5 could be shorten down significantly